TN17 said:Homework Statement
This is another question related to the vertical spring lab where we try to determine k, the spring constant.
When the vertical mass-spring system is at equilibrium, then the F in F = kx is equal to F = mg, or 9.8.
What would the F be in F = kx when the system is oscillating?
In that case, the only information we know from the experiment is x (the displacement) and mass of the object.
I'm not sure how to move on from there.
rock.freak667 said:When the mass is initial hung, there is an initial displacement δ, so you have kδ=mg
then you displace the mass a distance 'x' such that the spring force acting is k(δ+x).
TN17 said:I understand the first part that you said.
And the second part, do you mean that F = k(δ+x)?
Okay.rock.freak667 said:right, that F is the spring force which is just one of the forces acting when you displace the mass an additional distance x. You will still have the weight mg acting downwards.
TN17 said:Okay.
But if the purpose was to find k, the spring constant, how would I do so when I only know δ and x?
That's the part I'm confused about from your equation.
Simple Harmonic Motion (SHM) is a type of periodic motion in which the restoring force is directly proportional to the displacement from the equilibrium position. This means that as the object moves away from its equilibrium position, the restoring force will increase, causing the object to return to its original position. Examples of SHM include the motion of a pendulum and the vibrations of a mass on a spring.
In a vertical spring lab, the spring is used to create SHM by suspending a mass from the spring and measuring its oscillations. By measuring the period of the oscillations and the mass, the spring constant (k) can be calculated using the equation T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.
The spring constant (k) is a measure of the stiffness of the spring and is essential in understanding its behavior. It helps in predicting the motion of the object attached to the spring and can also be used to determine the force exerted by the spring on the object. Additionally, the spring constant is a fundamental property of the spring and can be used to compare different springs.
Several factors can affect the accuracy of finding the spring constant (k) in a vertical spring lab, such as the precision of the measuring equipment, air resistance, and friction in the spring. The accuracy can also be impacted by the mass used, as well as any external forces acting on the object during its oscillations.
The principles of SHM and the spring constant (k) are essential in a wide range of real-world applications. For example, they are used in the design of suspension systems in cars and buildings, as well as in the development of shock absorbers and other damping devices. The results of a vertical spring lab can also be used to understand and analyze the behavior of mechanical systems, such as pendulums and vibrating systems.